Finite Group DatabasebetaFinite Group DatabasebetaOrder 5888.
134 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 134 conjugacy classes of subgroups — too many to draw. Only its 58 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C23 | C2×D32 |
| commutator, Frattini, cosocle | C32 | C23×C23 |
| LCS | G ▷ C32 ▷ C16 ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C23 ◁ C2×C4×C23 ◁ C2×C8×C23 ◁ C2×C16×C23 ◁ C2×C23×C32 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C23×#2262 | C2 | semidirect |
| 2. C2×C23×D32 | C2 | semidirect |
| 3. C23×SD128 | C2 | semidirect |
| 4. C23×D64 | C2 | semidirect |
| 5. C23×M128 | C2 | semidirect |
| 8. C23×Q64 | C22 | semidirect |
| 12. C23×D32 | C22 | semidirect |
| 14. C23×C64 | C22 | semidirect |
| 35. #13742 | C23 | direct (N × H) |
| 46. #2262 | C2×C23 | semidirect |
| 47. C2×D32 | C2×C23 | semidirect |
| 48. SD128 | C2×C23 | semidirect |
| 49. D64 | C2×C23 | semidirect |
| 50. M128 | C2×C23 | semidirect |
| 60. Q64 | C22×C23 | semidirect |
| 64. D32 | C22×C23 | semidirect |
| 66. C64 | C22×C23 | semidirect |
| 81. C23 | #13742 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#2262 | 2 |
| C2×C23×D32 | 2 |
| C23×SD128 | 2 |
| C23×D64 | 2 |
| C23×M128 | 2 |
| #13742 | 23 |